Summary
International Symposium on Nonlinear Theory and Its Applications
2016
Session Number:A4L-G
Session:
Number:A4L-G-5
Interval Estimation of Coupling Delay Time from Phase Time Series
Boris Bezruchko, Elena Sidak, Dmitry Smirnov,
pp.-
Publication Date:2016/11/27
Online ISSN:2188-5079
Summary:
We consider interval estimation of a time delay in coupling between oscillatory systems from observed time series. It is shown that asymptotic estimates, based on an empiric model in the form of first-order phase oscillators and maximum likelihood formalism, can lead to false conclusions about the value of the delay in two cases: (i) for nonlinear low-dimensional systems whose phases are well-defined but considerable amplitude fluctuations make phase description of the dynamics insufficient, (ii) for systems whose phases are not well-defined due to large amplitude fluctuations. We suggest an empirical criterion for diagnosis of such problematic situations and develop a modified estimator assuring low probability of false conclusions in those situations. Efficiency of the suggested estimator is demonstrated for benchmark systems with different dynamical properties, including stochastic and deterministically chaotic oscillators. An application of the approach to an analysis of large-scale climate processes is presented.